Chapter SH, Problem 20.12APP

To determine

To calculate: Amount of energy converted in one year and mass equivalent to that energy.

Answer to Problem 20.12APP

Amount of energy converted in one year is $252288000\text{ billion J}$ and mass equivalent to this energy is 2.8 kg.

Explanation of Solution

Given:

The power plant converts approximately $8\text{ billion J}$ of nuclear energy into electrical energy every second.

Formula used:

Mass energy relation is given by,

  $E=m{c}^2$

where m is mass and c is speed of light in vacuum.

Calculation:

There are 31536000 seconds in a year.

Therefore, amount of energy converted in one year = $8\times 31536000=252288000\text{ billion J}$

Mass equivalent to this energy is calculated as:

  $\begin{array}{l}E=m{c}^2\\ m=\frac{E}{c^2}\\ m=\frac{252288000\times {10}^9\text{ J}}{{\left(3\times {10}^8\text{ m/s}\right)}^2}\\ m=2.8\text{ kg}\end{array}$

Conclusion:

Amount of energy converted in one year is $252288000\text{ billion J}$ and mass equivalent to this energy is 2.8 kg.